Question

Find the probability that a person has an IQ greater than 120. Include a sketch of the graph and shade the area under the normal curve corresponding to this probability. Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization. Sketch the graph and shade the area under the curve corresponding to this score and above. IQ scores between 90 and 110 are considered to be within the normal or average range of intelligence. What is the probability that a person chosen at random will have an IQ score between 90 and 110? Sketch the graph and shade the area under the curve corresponding to this probability.

IQ is normally distributed with a mean of 100 and a standard deviation of 15.

•Find the probability that a person has an IQ greater than 120. Include a sketch of the graph and shade the area under the normal curve corresponding to this probability.

•Mensa is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the Mensa organization. Sketch the graph and shade the area under the curve corresponding to this score and above.

•IQ scores between 90 and 110 are considered to be within the normal or average range of intelligence. What is the probability that a person chosen at random will have an IQ score between 90 and 110? Sketch the graph and shade the area under the curve corresponding to this probability.

Answer 1

Ans:

1)

z=(120-100)/15

z=1.33

P(z>1.33)=0.0912

0.4 0.3 0.2 0.1 0.0 4 -1 -3 -2 0 1 2

2)

P(Z>z)=0.02

P(Z<=z)=1-0.02=0.98

z=normsinv(0.98)=2.054

minimum IQ=100+2.054*15=130.8

0.4 0.3 0.2 0.1 0.0 -4 3 2 10 -1 -3 2

3)

z(90)=(90-100)/15=-0.67

z(110)=(110-100)/15=0.67

P(-0.67<z<0.67)=P(z<0.67)-P(z<-0.67)

=0.7475-0.2525=0.4950

-4 -3 -2 -1 C 2 3 4